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A Moderate Attribute Reduction Approach in Decision-Theoretic Rough Set

  • Hengrong Ju
  • Xibei Yang
  • Pei Yang
  • Huaxiong Li
  • Xianzhong Zhou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9437)

Abstract

Attribute reduction is an important topic in Decision-Theoretic Rough Set theory. To overcome the limitations of lower-approximation-monotonicity based reduct and cost minimum based reduct, a moderate attribute reduction approach is proposed in this paper, which combines the lower approximation monotonicity criterion and cost minor criterion. Furthermore, the proposed attribute reduct is searched by solving an optimization problem, and a fusion fitness function is proposed in a generic algorithm, such that the reduct is computed in a low time complexity. Experimental analysis is included to validate the theoretic analysis and quantify the effectiveness of the proposed attribute reduction algorithm. This study indicates that the optimality is not the best and sub-optimum may be the best choice.

Keywords

Attribute reduction Decision cost DTRS Lower-approximation-monotonicity 

Notes

Acknowledgment

This work is supported by the Natural Science Foundation of China (Nos. 61100116, 71201076, 61170105, 61473157,71171107), Qing Lan Project of Jiangsu Province of China, and the Ph.D. Programs Foundation of Ministry of Education of China (20120091120004).

References

  1. 1.
    Yao, Y.Y., Wong, S.K.M., Lingras, P.: A decision-theoretic rough set model. In: Ras, Z.W., Zemankova, M., Emrich, M.L. (eds.) Methodologies for Intelligent Systems, vol. 5, pp. 17–24. North-Holland, New York (1990)Google Scholar
  2. 2.
    Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. Int. J. Man Mach. Stud. 37, 793–809 (1992)CrossRefGoogle Scholar
  3. 3.
    Jia, X.Y., Tang, Z.M., Liao, W.H., et al.: On an optimization representation of decision-theoretic rough set model. Int. J. Approx. Reason. 55, 156–166 (2014)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Li, H., Zhou, X., Zhao, J., Huang, B.: Cost-sensitive classification based on decision-theoretic rough set model. In: Li, T., Nguyen, H.S., Wang, G., Grzymala-Busse, J., Janicki, R., Hassanien, A.E., Yu, H. (eds.) RSKT 2012. LNCS, vol. 7414, pp. 379–388. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  5. 5.
    Li, H., Zhou, X., Huang, B., Liu, D.: Cost-sensitive three-way decision: a sequential strategy. In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds.) RSKT 2013. LNCS, vol. 8171, pp. 325–337. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  6. 6.
    Liang, D.C., Liu, D., Pedrycz, W., Hu, P.: Triangular fuzzy decision-theoretic rough sets. Int. J. Approx. Reason. 54, 1087–1106 (2013)CrossRefGoogle Scholar
  7. 7.
    Liang, D.C., Liu, D.: Systematic studies on three-way decisions with interval-valued decision-theoretic rough sets. Inform. Sci. 276, 186–203 (2014)CrossRefGoogle Scholar
  8. 8.
    Liu, D., Li, T.R., Li, H.X.: A multiple-category classification approach with decision-theoretic rough sets. Fundam. Inform. 115, 173–188 (2012)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Liu, D., Li, T.R., Liang, D.C.: Incorporating logistic regression to decision-theoretic rough sets for classification. Int. J. Approx. Reason. 55(1), 197–210 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Yu, H., Liu, Z.G., Wang, G.Y.: An automatic method to determine the number of clusters using decision-theoretic rough set. Int. J. Approx. Reason. 55, 101–115 (2014)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Qian, Y.H., Zhan, G.H., Sang, Y.L., et al.: Multigranulation decision-theoretic rough sets. Int. J. Approx. Reason. 55, 225–237 (2013)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Li, W.T., Xu, W.H.: Double-quantitative decision-theoretic rough set. Inform. Sci. 316, 54–67 (2015)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Li, W.T., Xu, W.H.: Multigranulation decision-theoretic rough set in ordered information system. Fundam. Inform. 139, 67–89 (2015)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Li, W., Xu, W.: Probabilistic rough set model based on dominance relation. In: Miao, D., Pedrycz, W., Slezak, D., Peters, G., Hu, Q., Wang, R. (eds.) RSKT 2014. LNCS, vol. 8818, pp. 856–864. Springer, Heidelberg (2014) Google Scholar
  15. 15.
    Ju, H.R., Yang, X.B., Song, X.N., et al.: Dynamic updating multigranulation fuzzy rough set: approximations and reducts. Int. J. Mach. Learn. Cyber. 5(6), 981–990 (2014)CrossRefGoogle Scholar
  16. 16.
    Ju, H.R., Yang, X.B., Dou, H.L., et al.: Variable precision multigranulation rough set and attributes reduction. Trans. Rough Set 8, 52–68 (2014)zbMATHGoogle Scholar
  17. 17.
    Zhao, Y., Wong, S.K.M., Yao, Y.: A note on attribute reduction in the decision-theoretic rough set model. In: Peters, J.F., Skowron, A., Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) Transactions on Rough Sets XIII. LNCS, vol. 6499, pp. 260–275. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  18. 18.
    Ma, X.A., Wang, G.Y., Yu, H., et al.: Decision region distribution preservation reduction in decision-theoretic rough set model. Inform. Sci. 278, 614–640 (2014)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Yao, Y.Y., Zhao, Y.: Attribute reduction in decision-theoretic rough set models. Inform. Sci. 178, 3356–3373 (2008)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Li, H.X., Zhou, X.Z., Zhao, J.B., et al.: Non-monotonic attribute reduction in decision-theoretic rough sets. Fundam. Inform. 126(4), 415–432 (2013)MathSciNetzbMATHGoogle Scholar
  21. 21.
    Jia, X.Y., Liao, W.H., Tang, Z.M., et al.: Minimum cost attribute reduction in decision-theoretic rough set models. Inform. Sci. 219, 151–167 (2013)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Yang, X.B., Song, X.N., Chen, Z.H., et al.: On multigranulation rough sets in incomplete information system. Int. J. Mach. Learn. Cyb. 3, 223–232 (2012)CrossRefGoogle Scholar
  23. 23.
    Yang, X.B., Qi, Y.S., Song, X.N., et al.: Test cost sensitive multigranulation rough set: model and minimal cost selection. Inform. Sci. 250, 184–199 (2013)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Yang, X.B., Song, X.N., She, Y.H., et al.: Hierarchy on multigranulation structures: a knowledge distance approach. Int. J. Gen. Syst. 42(7), 754–773 (2013)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Yao, Y.Y.: Probabilistic rough set approximations. Int. J. Approx. Reason. 49, 255–271 (2008)CrossRefGoogle Scholar
  26. 26.
    Yao, Y.: Three-way decision: an interpretation of rules in rough set theory. In: Wen, P., Li, Y., Polkowski, L., Yao, Y., Tsumoto, S., Wang, G. (eds.) RSKT 2009. LNCS, vol. 5589, pp. 642–649. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  27. 27.
    Yao, Y., Zhou, B.: Naive Bayesian rough sets. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds.) RSKT 2010. LNCS, vol. 6401, pp. 719–726. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  28. 28.
    Yang, X., Qi, Y., Yu, H., Yang, J.: Want more? Pay more!. In: Cornelis, C., Kryszkiewicz, M., Ślȩzak, D., Ruiz, E.M., Bello, R., Shang, L. (eds.) RSCTC 2014. LNCS, vol. 8536, pp. 144–151. Springer, Heidelberg (2014) Google Scholar

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Authors and Affiliations

  • Hengrong Ju
    • 1
    • 2
  • Xibei Yang
    • 2
  • Pei Yang
    • 1
    • 3
    • 4
  • Huaxiong Li
    • 1
    • 4
  • Xianzhong Zhou
    • 1
    • 4
  1. 1.School of Management and EngineeringNanjing UniversityNanjingPeople’s Republic of China
  2. 2.School of Computer Science and EngineeringJiangsu University of Science and TechnologyZhenjiangPeople’s Republic of China
  3. 3.State Key Laboratory for Novel Software TechnologyNanjing UniversityNanjingPeople’s Republic of China
  4. 4.Research Center for Novel Technology of Intelligent EquipmentsNanjing UniversityNanjingPeople’s Republic of China

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